Flocks of topological circle planes

Abstract

Abstract We prove that every flock of a finite-dimensional locally compact connected circle plane is homeomorphic to ℝ or 1 and that every flock of a real Miquelian circle plane defines a compact 4-dimensional translation plane. Furthermore we investigate (topological) properties of regulizations. These properties are used to relate the automorphism group of a flock to the automorphism group of the corresponding translation plane.